Fundamental Limits of Communications in Interference Networks-Part III: Information Flow in Strong Interference Regime

This paper, as the continuation of Parts I and II on Fundamental Limits of Communication in Interference Networks, is related to the study of information flow in networks with strong interference. First, the concept of strong interference is more broadly defined: a network is said to be in the strong interference regime when the coding scheme achieving the capacity region is such that each receiver decodes all transmitted messages by its connected transmitters. Next, conditions under which the strong interference regime holds are explored. The two-receiver networks are considered initially. A unified outer bound for the capacity region of these networks is established. It is shown that this outer bound can be systematically translated into simple and computable capacity outer bounds for special cases such as the twouser Classical Interference Channel (CIC) and the Broadcast Channel with Cognitive Relays (BCCR) with common information. For these channels, special cases are presented where our outer bounds are tight, which yield the exact capacity. More importantly, by using the derived outer bounds, a strong interference regime is identified for the general two-receiver interference networks with any arbitrary topology. This strong interference regime, which is represented by only two conditions, includes all previously known results for simple topologies such as the two-user CIC, the cognitive radio channel, and many others. Then, networks with arbitrary number of receivers are considered. Finding non-trivial strong interference regime for such networks, specifically for the CICs with more than two users, has been one of the open problems in network information theory. In this paper, we will give a solution to this problem. Specifically, a new approach is developed based on which one can obtain strong interference regimes not only for the multi-user CICs but also for any interference network of arbitrary large sizes. To this development, some new lemmas are proved which have a central role in the derivations. As a result, this paper establishes the first non-trivial capacity result for the multi-user classical interference channel. A general formula is also presented to derive strong interference conditions for any given network topology. In fact, for the first time in the history of network information theory, we establish a capacity result for a general single-hop communication network regardless of that how much its topology is complex.